A shape error metric for sheet metal forming and its application to springback

There are many variations within sheet metal forming, some of which are manifest in the final geometry of the formed component. It is important that this geometric variation be quantified and measured for use in a process or quality control system. The contribution of this paper is to propose a novel way of measuring the geometric difference between the desired shape and an actual formed "U" channel. The metric is based upon measuring errors in terms of the significant manufacturing variations. The metric accords with the manually measured errors of the channel set. The shape error metric is then extended to develop a simple empirical, whole-component, springback error measure. The springback error measure combines into one value all the angle springback and side wall curl geometric errors for a single channel. Two trends were observed: combined springback decreases when the blank holder force is increased; and the combined springback marginally decreases when the die radii is increased.

Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming

To quantify the frictional behaviour in sheet forming operations, several laboratory experiments which simulate the real forming conditions are performed. The Bending Under Tension Test is one such experiment which is often used to represent the frictional flow of sheet material around a die or a punch radius. Different mathematical representations are used to determine the coefficient of friction in the Bending Under Tension Test. In general the change in the strip thickness in passing over the die radius is neglected and the radius of curvature to thickness ratio is assumed to be constant in these equations. However, the effect of roller radius, sheet thickness and the surface pressure are also omitted in some of these equations. This work quantitatively determined the effect of roller radius and the tooling pressure on the coefficient of friction. The Bending Under Tension Test was performed using rollers with different radii and also lubricants with different properties. The tool radii were found to have a direct influence in the contact pressure. The effect of roller radius on friction was considerable and it was observed that there is a clear relationship between the contact pressure and the coefficient of friction.

Improving an inverse model of sheet metal forming by neural network based regression

An inverse model for a sheet meta l forming process aims to determine the initial parameter levels required to form the final formed shape. This is a difficult problem that is usually approached by traditional methods such as finite element analysis. Formulating the problem as a classification problem makes it possible to use well established classification algorithms, such as decision trees. Classification is, however, generally based on a winner-takes-all approach when associating the output value with the corresponding class. On the other hand, when formulating the problem as a regression task, all the output values are combined to produce the corresponding class value. For a multi-class problem, this may result in very different associations compared with classification between the output of the model and the corresponding class. Such formulation makes it possible to use well known regression algorithms, such as neural networks. In this paper, we develop a neural network based inverse model of a sheet forming process, and compare its performance with that of a linear model. Both models are used in two modes, classification mode and a function estimation mode, to investigate the advantage of re-formulating the problem as a function estimation. This results in large improvements in the recognition rate of set-up parameters of a sheet metal forming process for both models, with a neural network model achieving much more accurate parameter recognition than a linear model.

Contact pressure and wear in sheet metal forming - an FEM analysis

Wear is the principal cause of tool failure in most sheet metal forming processes. It is well known that the contact pressure between the blank and the tool has a large influence on the wear of the tool, and hence the tool life. This investigation utilises the finite element method to analyse the contact pressure distribution over the die radius for a particular deep drawing process. Furthermore, the evolution of the predicted contact pressure distribution throughout the entire stroke of the punch is also examined. It was found that the majority of the process shows a steady state pressure distribution, with two characteristic peaks over the die radius, at the beginning and end of the sheet contact area. Interestingly, the initial transient contact pressure response showed extremely high localised peak pressures; more than twice that of the steady state peaks. Results are compared to wear reported in the literature, during similar experimental deep drawing processes. Finally, the significance and effect of the results on wear and wear-testing techniques are discussed.

Modeling of contact pressure in sheet metal forming

For a given sheet metal forming process, an accurate determination of the contact pressure distribution experienced is an essential step towards the estimation of tool life. This investigation utilizes finite element (FE) analysis to determine the evolution and distribution of contact pressure over the die radius, throughout the duration of a channel forming process. It was found that a typical two-peak steady-state contact pressure response exists for the majority of the process. However, this was preceded by a transient  response, which produced extremely large and localized contact pressures. Notably, it was found that the peak transient contact pressure was more than double the steady-state peak. These contact pressure results may have a significant influence on the tool wear response and therefore impact current wear testing and prediction techniques. Hence, an investigation into the validity of the predicted contact pressure was conducted.

The influence of temperature on the forming behavior of metal/polymer laminates in sheet metal forming

The influence of temperature on the forming behavior of an aluminum/polypropylene/aluminum (APA) sandwich sheet was studied. Shear and tensile tests were performed to determine the mechanical properties of the laminate and the component materials as a function of process temperature. The forming limit diagram (FLD) of the laminate was established for two different temperatures, and its springback behavior was examined in four-point bend and channel bend tests. Cup forming tests were performed at various test temperatures to determine the limiting drawing ratio (LDR) and the tendency for wrinkling at these temperatures. Although there was only a minor influence of temperature on the mechanical properties and the FLD values of the laminate, the bend test results reveal that springback can be reduced by forming at higher temperature. The decreasing strength of the core material with rising process temperature led to an increased tendency of the laminate to wrinkle in the heated cup drawing tests.

Knowledge based optimisation techniques for sheet metal forming die design

A knowledge based optimism technique has been developed to predict solutions for quality issues found in an initial draw die design. Post processing of the initial design yields all the features applying forces, and major quality issues. Using the geometric relationship between the two, a knowledge-base is interrogated to determine the possible corrective actions. These actions are then passed through a fast semi-analytical model to determine the level of change required. Results from a 2D forming are presented to highlight the advantage of the new algorithms over current optimisation techniques.

Multivariate modelling of variability in sheet metal forming

The inherent variability in incoming material and process conditions in sheet metal forming makes quality control and the maintenance of consistency extremely difficult. A single FEM simulation is successful at predicting the formability for a given system, however lacks the ability to capture the variability in an actual production process due to the numerical deterministic nature. This paper investigates a probabilistic analytical model where the variation of five input parameters and their relationship to the sensitivity of springback in a stamping process is examined. A range of sheet tensions are investigated, simulating different operating windows in an attempt to highlight robust regions where the distribution of springback is small. A series of FEM simulations were also performed, to compare with the findings from the analytical model using AutoForm Sigma v4.04 and to validate the analytical model assumptions.

Results show that an increase in sheet tension not only decreases springback, but more importantly reduces the sensitivity of the process to variation. A relative sensitivity analysis has been performed where the most influential parameters and the changes in sensitivity at various sheet tensions have been investigated. Variation in the material parameters, yield stress and n-value were the most influential causes of springback variation, when compared to process input parameters such as friction, which had a small effect. The probabilistic model presented allows manufacturers to develop a more comprehensive assessment of the success of their forming processes by capturing the effects of inherent variation.

Statistical analysis of finite element modeling in sheet metal forming and springback analysis

This work focuses on development of a method to statistically study forming and springback problems of TRansformation Induced Plasticity (TRIP) through an industrial case study. A Design of Experiments (DOE) approach was used to study the sensitivity of predictions to four user input parameters in implicit and explicit sheet metal forming codes. Numerical results were compared to experimental measurements of parts stamped in an industrial production line. The accuracy of forming strain predictions for TRIP steel were comparable with conventional steel, but the springback predictions of TRIP steel were far less accurate. The statistical importance of selected parameters for forming and springback prediction is also discussed. Changes of up to ±10% in Young's modulus and coefficient of friction were found to be insignificant in improving or deteriorating the statistical correlation of springback accuracies.

Contact pressure evolution and its relation to wear in sheet metal forming

For a given sheet metal forming process, an accurate determination of the contact pressure distribution is an essential step towards the estimation of tool life. This investigation utilizes finite element (FE) analysis to model and explain the evolution and distribution of contact pressure over the die radius, throughout the duration of a channel forming process. It was found that a typical two-peak steady-state contact pressure response exists for the majority of the process. However, this was preceded by an initial transient response, characterized by extremely large and localized contact pressures, which were more than double the magnitude of the steady-state peak pressure. The validity of the predicted contact pressure behavior was assessed via detailed numerical analysis and by examining the wear response of an experimental stamping operation. The experimental results revealed that the high contact pressure zones of the transient response corresponded to a severe galling wear mechanism. Therefore, the transient response may be of primary significance to the tool wear response; thus questioning the applicability of traditional bending-under-tension wear tests for sheet metal stamping processes. Finally, a parametric study was conducted, examining the influence of the major process parameters on the steady-state and peak transient contact pressures, using the developed FE model. It was found that the bend ratio and the blank material ultimate tensile strength had the most influence on the peak contact pressures. The main process-related parameters, friction coefficient and blank holder force, were found to have only a minor influence.

Contact pressure prediction in sheet metal forming using finite element analysis

Tool wear has become a significant issue associated with the forming of high strength sheet steels in the automotive industry. In order to combat this problem, recent research has been devoted to utilizing the contact results obtained from current sheet metal forming software predictions, in order to develop/apply tool wear models or tool material selection criteria for use in the stamping plant. This investigation aims to determine whether a specialized sheet metal forming software package can correctly capture the complex contact conditions that occur during a typical sheet metal stamping process. The contact pressure at the die radius was compared to results obtained using a general-purpose finite element software package, for a simple channel-forming process. Although some qualitative similarities between the two predictions were observed, it was found that significant differences in the magnitude and distribution of the contact pressure exists. The reasons for the discrepancies in results are discussed with respect to the simplifications and assumptions adopted in the finite element model definitions, and with regards to other results available in the literature.